4a(2a+2)-17=15

Simple and best practice solution for 4a(2a+2)-17=15 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for 4a(2a+2)-17=15 equation: 


Simplifying
4a(2a + 2) + -17 = 15

Reorder the terms:
4a(2 + 2a) + -17 = 15
(2 * 4a + 2a * 4a) + -17 = 15
(8a + 8a2) + -17 = 15

Reorder the terms:
-17 + 8a + 8a2 = 15

Solving
-17 + 8a + 8a2 = 15

Solving for variable 'a'.

Reorder the terms:
-17 + -15 + 8a + 8a2 = 15 + -15

Combine like terms: -17 + -15 = -32
-32 + 8a + 8a2 = 15 + -15

Combine like terms: 15 + -15 = 0
-32 + 8a + 8a2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-4 + a + a2) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(-4 + a + a2)' equal to zero and attempt to solve:

Simplifying
-4 + a + a2 = 0

Solving
-4 + a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + a + 4 + a2 = 0 + 4

Reorder the terms:
-4 + 4 + a + a2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + a + a2 = 0 + 4
a + a2 = 0 + 4

Combine like terms: 0 + 4 = 4
a + a2 = 4

The a term is a.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
a + 0.25 + a2 = 4 + 0.25

Reorder the terms:
0.25 + a + a2 = 4 + 0.25

Combine like terms: 4 + 0.25 = 4.25
0.25 + a + a2 = 4.25

Factor a perfect square on the left side:
(a + 0.5)(a + 0.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(a + 0.5) equal to 2.061552813 and -2.061552813.


Subproblem 1
a + 0.5 = 2.061552813

Simplifying
a + 0.5 = 2.061552813

Reorder the terms:
0.5 + a = 2.061552813

Solving
0.5 + a = 2.061552813

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-0.5' to each side of the equation.
0.5 + -0.5 + a = 2.061552813 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + a = 2.061552813 + -0.5
a = 2.061552813 + -0.5

Combine like terms: 2.061552813 + -0.5 = 1.561552813
a = 1.561552813

Simplifying
a = 1.561552813


Subproblem 2
a + 0.5 = -2.061552813

Simplifying
a + 0.5 = -2.061552813

Reorder the terms:
0.5 + a = -2.061552813

Solving
0.5 + a = -2.061552813

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-0.5' to each side of the equation.
0.5 + -0.5 + a = -2.061552813 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + a = -2.061552813 + -0.5
a = -2.061552813 + -0.5

Combine like terms: -2.061552813 + -0.5 = -2.561552813
a = -2.561552813

Simplifying
a = -2.561552813


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {1.561552813, -2.561552813}
Solution
a = {1.561552813, -2.561552813}

See similar equations:

| 3-(x+7)=2x+1 | | 5+9x=130 | | .18y+.05(y+6000)=2140 | | (x^2-9x)-(5x^2-7x)=4x^2-2x | | 5(4+r)=20+5r | | (j-30)+(j+15)+(j)=595 | | -7-2n=7(-8n-2)+7 | | 4(x-8)=5x | | -30=8t | | -5+5(3-7d)+5d=-20 | | 20+85y=120 | | 6x-4=2(2)+4 | | 7y-5x=14 | | -8=-8(5+b) | | (6(2)-4)=(2(2)+4) | | (6x-4)=(2(2)+4) | | 64+80t-16t^2=0 | | 3x^4-22x^2=0 | | 35x+.08x=25x+.25x | | p-20=8p-8 | | s[-4]=7.3 | | 5(15x-3)=45x-15 | | 7/8=1/4p | | -2(x+1)-4x=16-6(x+3) | | 5x+2=-188 | | -2p-2(5-4p)=4(p-4)-14 | | 3k^3+3k=10k^2 | | 6x-8=5x-8 | | 24+3.00x=1.50 | | -11+10(x+10)=2-5(2p+11) | | h+8=31 | | -6-3(x-1)=-2(-5-5x) |

Equations solver categories